Q. 34.3( 9 Votes )

# In a right triang

Answer :

Given Δ ABC, right angled at B, BC = 12 cm and AB = 5 cm.

There is a circle inscribed in the triangle as follows: Let radius of the circle be r cm.

We know that by Pythagoras Theorem, AC2 = AB2 + BC2

In Δ ABC,

AC2 = 122 + 52

AC2 = 144 + 25

AC2 = 169

AC = 13

From the figure,

Ar (ΔABC) = ar (ΔAOC) + ar (ΔAOB) + ar (ΔBOC)

1/2 (AB) (AC) = 1/2 (OP) (AC) + 1/2 (OQ) (BC) + 1/2 (OR) (AB)

1/2 (12) (5) = 1/2 (r) (5) + 1/2 (r) (13) + 1/2 (r) (12)

1/2 (12) (5) = 1/2 (r) (5 + 13 + 12)

(12) (5) = r (30)

r = 2 cm

The radius of the circle inscribed in the given triangle is 2 cm.

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